from manim import *
class CustomCurve(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [15, 20, 0],
            [14,15,0],
            [10, 12.5, 0],
            [14,10,0],
            [15, 5, 0],
            
        ]
        self.set_points_smoothly(points)

class CustomCurve1(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [25, -15, 0],
            [20,-20,0],
            [25,-25,0],
        ]
        self.set_points_smoothly(points)



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子

        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        
        text = Tex(r"$\int _{0}^{\pi }\dfrac{x}{2+\sin x}dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        text3 = Tex(r"\text{芳900例1:}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text,LEFT,buff=1)
        text1 = Tex(
                   r"$f\left( x\right) =\dfrac{1}{2+\sqrt{1-x^{2}}}+\dfrac{1}{1+\cos \dfrac{\pi }{2}x+2\sin \dfrac{\pi }{2}x}\int _{0}^{1}f\left( x\right) dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([5,5,0])
        text4 = Tex(
                   r"\text{芳900例2:}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-35,6,0])
        text2 = Tex(r"\text{求}$f\left( x\right)$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-23,-2,0])
        self.play(Write(text),self.camera.frame.animate.scale(0.9),Write(text3))
        
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        self.play(text.animate().scale(1).shift(LEFT*12),text3.animate().scale(1).shift(LEFT*12)) 
        #第一步
        text50 = Tex(
                   r"\text{注：}$\int _{0}^{\pi }xf\left( \sin x\right) dx=\pi \int ^{\frac{\pi }{2}}_{0}f\left( \sin x\right) dx$",color=PINK
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text,RIGHT,buff=4)
        self.play(Write(text50))
        text5 = Tex(
                   r"$=\pi \int _{0}^{\frac{\pi }{2}}\dfrac{1}{2+\sin x}dx$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text3,DOWN,buff=2)
        self.play(Write(text5))
        #第二步
        text60 = Tex(
                   r"\text{令}$t=\tan \dfrac{x}{2}$",color=PINK
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text5,RIGHT,buff=2)
        self.play(Write(text60))
        text6 = Tex(
                   r"$=\pi \int _{0}^{1}\dfrac{1}{t^{2}+t+1}dt$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text5,DOWN,buff=2)
        self.play(Write(text6))
        #第三步
        text70 = Tex(
                   r"\text{(配方)}",color=PINK
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text6,RIGHT,buff=2)
        self.play(Write(text70))
        text7 = Tex(
                   r"$=\pi \int ^{1}_{0}\dfrac{1}{\left( t+\dfrac{1}{2}\right) ^{2}+\left( \dfrac{\sqrt{3}}{2}\right) ^{2}}d\left( t+\dfrac{1}{2}\right) $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text6,DOWN,buff=2)
        self.play(Write(text7))
        #第四步
        text80 = Tex(
                   r"\text{注：}$\int \dfrac{1}{x^{2}+a^{2}}ax=\dfrac{1}{a}\arctan \dfrac{x}{a}+c$",color=PINK
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text7,RIGHT,buff=2)
        self.play(Write(text80))
        text8 = Tex(
                   r"$ =\pi \cdot \dfrac{2}{\sqrt{3}}\arctan \dfrac{2t+1}{\sqrt{3}}| _{0}^{1}$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text7,DOWN,buff=2)
        self.play(Write(text8))
        #第五步
        text9 = Tex(
                   r"$=\dfrac{\sqrt{3}}{9}\pi ^{2}$",color=ORANGE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text8,DOWN,buff=2)
        self.play(Write(text9))



        self.wait()